Binary Darboux Transformation for the Sasa-Satsuma Equation

TL;DR

This paper develops binary Darboux transformations for the Sasa-Satsuma equation, enabling explicit construction of solutions like solitons and breathers, which are relevant in optical applications.

Contribution

It introduces a novel binary Darboux transformation framework for the Sasa-Satsuma equation and constructs explicit quasigrammian solutions.

Findings

Explicit soliton and breather solutions derived

Binary Darboux transformations applied to higher-order NLS equations

New solution methods for integrable equations in optics

Abstract

The Sasa-Satsuma equation is an integrable higher-order nonlinear Schr\"odinger equation. Higher-order and multicomponent generalisations of the nonlinear Schr\"odinger equation are important in various applications, e.g., in optics. One of these equations is the Sasa-Satsuma equation. We present the binary Darboux transformations for the Sasa-Satsuma equation and then construct its quasigrammians solutions by iterating its binary Darboux transformations. Periodic, one-soliton, two-solitons and breather solutions are given as explicit examples.